Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions

In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functi...

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Veröffentlicht in:Mathematical notes (Miskolci Egyetem (Hungary)) Jg. 24; H. 2; S. 553 - 568
Hauptverfasser: Ali, Muhammad Aamir, Soontharanon, Jarunee, Budak, Hüseyin, Sitthiwirattham, Thanin, Fečkan, Michal
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Miskolc University of Miskolc 2023
Schlagworte:
Calculus
Convex analysis
Convexity
Estimates
Inequalities
Integrals
R&D
Research & development
ISSN:1787-2405, 1787-2413
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Abstract In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Holder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.
AbstractList In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of functions. Moreover, we establish a new Simpson's type inequalities for differentiable convex functions with respect to a pair of functions. We also prove two more Simpson's type inequalities for differentiable convex functions with respect to a pair of functions using the power mean and Holder's inequalities. It is also shown that the newly established inequalities are the extension of some existing results. Finally, we add some mathematical examples and their graphs to show the validity of newly established results.
Author Budak, Hüseyin
Soontharanon, Jarunee
Ali, Muhammad Aamir
Sitthiwirattham, Thanin
Fečkan, Michal
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  fullname: Fečkan, Michal
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Snippet In this article, we establish two new and different versions of fractional Hermite-Hadamard type inequality for the convex functions with respect to a pair of...
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StartPage 553
SubjectTerms Calculus
Convex analysis
Convexity
Estimates
Inequalities
Integrals
R&D
Research & development
Title Fractional Hermite-Hadamard inequality and error estimates for Simpson's formula through convexity with respect to a pair of functions
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